Inferring the Focal Depths of Small Earthquakes in Southern California Using Physics-Based Waveform Features
Determining the depths of small crustal earthquakes is challenging in many regions of the world, because most seismic networks are too sparse to resolve trade-offs between depth and origin time with conventional arrival-time methods. Precise and accurate depth estimation is important, because it can help seismologists discriminate between earthquakes and explosions, which is relevant to monitoring nuclear test ban treaties and producing earthquake catalogs that are uncontaminated by mining blasts. Here, we examine the depth sensitivity of several physics-based waveform features for ~8000 earthquakes in southern California that have well-resolved depths from arrival-time inversion. We focus on small earthquakes (2 < M L < 4) recorded at local distances (<150 km), for which depth estimation is especially challenging. We find that differential magnitudes (M w /M L –M c ) are positively correlated with focal depth, implying that coda wave excitation decreases with focal depth. We analyze a simple proxy for relative frequency content, Φ≡log 10 (M 0 )+3log 10 (f c ), and find that source spectra are preferentially enriched in high frequencies, or “blue-shifted,” as focal depth increases. Here, we also find that two spectral amplitude ratios Rg 0.5–2 Hz/Sg 0.5–8 Hz and Pg/Sg at 3–8 Hz decrease as focal depth increases. Using multilinear regression with these features as predictor variables, we develop models that can explain 11%–59% of the variance in depths within 10 subregions and 25% of the depth variance across southern California as a whole. We suggest that incorporating these features into a machine learning workflow could help resolve focal depths in regions that are poorly instrumented and lack large databases of well-located events. Some of the waveform features we evaluate in this study have previously been used as source discriminants, and our results imply that their effectiveness in discrimination is partially because explosions generally occur at shallower depths than earthquakes.